Continuity of Superposition Operators on the Double Sequence Spaces L-p

Sağır Duyar B., Gungor N.

FILOMAT, vol.29, no.9, pp.2107-2118, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 9
  • Publication Date: 2015
  • Doi Number: 10.2298/fil1509107s
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2107-2118
  • Keywords: Superposition Operators, Continuity, Double Sequence Spaces, Pringsheim's convergent
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, we define the superposition operator P-g where g : N-2 x R -> R by P-g ((x(ks))) = 1 (k, s, x(ks)) for all real double sequence (x(ks)). Chew & Lee [4] and Petranuarat & Kemprasit [7] have characterized P-g : l(p) -> l(1) and P-g : l(p) -> l(q) where 1 <= p, q < infinity, respectively. The main goal of this paper is to construct the necessary and sufficient conditions for the continuity of P-g : L-p -> L-1 and P-g : L-p -> L-q where 1 <= p, q < infinity.